Finite Group Databasebeta

← #28401177

Subgroups — #28401177

Order 14464.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299153C211yesmaximal, characteristic, complemented
2#20299127C211yesmaximal, characteristic
3#20299007C211yesmaximal, characteristic, complemented
4#20298966C211yesmaximal, characteristic, complemented
5#20298957C211yesmaximal, characteristic, complemented
6#20298853C212yesmaximal, complemented
7#20298841C212yesmaximal
8Q16×Dic113C212yesmaximal, complemented
9SD16×Dic113C212yesmaximal, complemented
10#20298550C211yesmaximal, characteristic, complemented
11#497×C113C211yesmaximal, characteristic, complemented
12C2×#14268630C2212yes—
13#16813622C2211yescharacteristic
14#16813615—21no—
15#16813614C2211yescharacteristic
16#16813613—21no—
17#16813604—21no—
18#16813602—21no—
19#16813598C2212yes—
20#16813598C2211yescharacteristic
21#16813593C2211yescharacteristic
22Q8×Dic113C2211yescharacteristic
23Q8×Dic113C2212yes—
24#16813587—21no—
25D4×Dic113C2211yescharacteristic
26#16813582—21no—
27#16813580—21no—
28#16813578—21no—
29C42×D113C2211yescharacteristic
30#16813556C2212yes—
31#16813554C2212yes—
32#16813546C2212yes—
33#16813546C2212yes—
34#16813546C2212yes—
35#16813543C2212yes—
36#16813533C2211yescharacteristic
37C8×Dic113C2212yes—
38C2×Q16×C113C2212yes—
39C2×SD16×C113C2212yes—
40C4⋊Q8×C113C2211yescharacteristic
41#124×C113C2211yescharacteristic
42#97×C113C2211yescharacteristic
43C2×Dic226—21no—
44C2×C22⋊D113—21no—
45C22×Dic113—21no—
46C2×C4×D113D411yescharacteristic
47C2×C4×D113D411yescharacteristic
48C2×C4×D113C2311yescharacteristic
49#14268630—24no—
50C2×#11744751C2312yes—
51C4⋊Dic113—21no—
52C4⋊Dic113—22no—
53C4⋊Dic113—21no—
54C4⋊Dic113C2311yescharacteristic
55C4⋊Dic113C2311yescharacteristic
56C4⋊Dic113C2312yes—
57#14268626—21no—
58#14268626—21no—
59#14268626—21no—
60#14268626—22no—
61C22⋊Dic113—21no—
62C22⋊Dic113—21no—
63#14268624—22no—
64#14268624—21no—
65C4×Dic113—21no—
66C4×Dic113—22no—
67C4×Dic113D411yescharacteristic
68C4×Dic113D411yescharacteristic
69C4×Dic113C2311yescharacteristic
70C2×Q8×C113C2311yescharacteristic
71C2×Q8×C113C2312yes—
72C2×D4×C113C2311yescharacteristic
73Q16×C113—24no—
74SD16×C113—24no—
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C22⋊C4×C113—21no—
79C22⋊C4×C113—21no—
80C42×C113C2311yescharacteristic
81C23×C113—21no—
82C22×D113C2×D411yescharacteristic
83Q8×C113—22no—
84Q8×C113—22no—
85Q8×C113—22no—
86D4×C113—22no—
87C2×C4×C113—21no—
88C2×C4×C113—22no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2411yescharacteristic
92C22⋊D113—42no—
93C2×Dic113—22no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—42no—
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99C2×Dic113C2×D411yescharacteristic
100C4×D113—22no—
101C4×D113—22no—
102C4×D113—41no—
103Dic226—42no—
104C8×C113#4114yes—
105#11744751—22no—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113C22×D411yescharacteristic
110C2×D113—21no—
111C2×D113—21no—
112C2×D113—21no—
113C4×C113—21no—
114C4×C113—21no—
115C4×C113—41no—
116C4×C113—42no—
117C4×C113C2×#4112yes—
118Dic113—21no—
119Dic113—21no—
120Dic113—41no—
121Dic113—42no—
122Dic113—41no—
123Dic113#13712yes—
124C2×C113—81no—
125C2×C113#53211yescharacteristic
126C2×C113C2×#13711yescharacteristic
127C2×C113#57511yescharacteristic
128D113—41no—
129#3172—1131nomaximal, Sylow
130C113#317211yescharacteristic, complemented, Sylow
131#533—1131no—
132#529—1131no—
133#501—1131no—
134#497D11311yescharacteristic, complemented
135#491—1131no—
136#489—1131no—
137#470—1132no—
138#468—1132no—
139C4×Q16—1132no—
140C4×SD16—1132no—
141C4×M16—1131no—
142C2×Q16C2×D11312yes—
143C2×SD16C2×D11312yes—
144C2×M16—1132no—
145C4⋊Q8—1131no—
146C4⋊Q8C2×D11311yescharacteristic
147#126—2261no—
148#125—1131no—
149#125—2261no—
150#124C2×D11311yescharacteristic
151#123—2261no—
152C22⋊Q8—1131no—
153C22⋊Q8—1132no—
154C22⋊Q8—2261no—
155#121—1131no—
156C4×Q8—1131no—
157C4×Q8—1132no—
158C4×Q8—2261no—
159C4×D4—1131no—
160C4×D4—2261no—
161#117—2261no—
162#117—2261no—
163C2×C42—1131no—
164#107—1132no—
165#106—1132no—
166#103—1132no—
167#103—1132no—
168#103—1132no—
169#102—1132no—
170#97—1131no—
171#97C2×D11311yescharacteristic
172C4×C8—1132no—
173C2×Q8—2261no—
174C2×Q8C22×D11311yescharacteristic
175C2×Q8C22×D11312yes—
176C2×D4—2261no—
177C2×D4C22×D11311yescharacteristic
178C22×C4—1131no—
179C22×C4—1131no—
180C22×C4—1131no—
181C22×C4—2261no—
182Q16—24no—
183SD16—24no—
184M16—2264no—
185C2×C8—1132no—
186C2×C8C22×D11312yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—1132no—
190C4⋊C4—1131no—
191C4⋊C4—1131no—
192C4⋊C4—2261no—
193C4⋊C4—2262no—
194C4⋊C4—2261no—
195C4⋊C4—2262no—
196C4⋊C4—2261no—
197C4⋊C4—2261no—
198C4⋊C4—2261no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—2262no—
202C22⋊C4—2261no—
203C22⋊C4—2261no—
204C22⋊C4—2261no—
205C42—1131no—
206C42—1131no—
207C42—1131no—
208C42—2261no—
209C42—2262no—
210C42C22×D11311yescharacteristic
211C23—21no—
212C23—1131no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—4522no—
217D4—22no—
218D4—4522no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—1131no—
222C2×C4—1131no—
223C2×C4—1131no—
224C2×C4—4521no—
225C2×C4—4522no—
226C2×C4—2262no—
227C2×C4—2261no—
228C2×C4—2262no—
229C2×C4—2261no—
230C2×C4—2262no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4C23×D11311yescharacteristic
234C8—2262no—
235C8#1426864614yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—2261no—
240C22—2261no—
241C22—2261no—
242C22C2×D4×D11311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—1132no—
248C4—4521no—
249C4—4521no—
250C4—4522no—
251C4—2261no—
252C4—2261no—
253C4C2×#1426864612yes—
254C2—81no—
255C2—4521no—
256C2#2029914611yescharacteristic
257C2#137×D11311yescharacteristic
258C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radical#16813593C22
hypercenter#497D113
hypocenterC113#3172
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20299007C2semidirect
4. #20298966C2semidirect
5. #20298957C2semidirect
6. #20298853C2semidirect
8. Q16×Dic113C2semidirect
9. SD16×Dic113C2semidirect
10. #20298550C2semidirect
11. #497×C113C2semidirect
130. C113#3172semidirect
134. #497D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202991532
#202991272
#202990072
#202989662
#202989572
#202988532
#202988412
Q16×Dic1132
SD16×Dic1132
#202985502
#497×C1132
#3172113